Appendix

GENERAL INSTRUCTIONS

This is an experiment in the economics of strategic decision making. Various research agencies have provided funds for this research. The instructions are simple. If you follow them closely and make appropriate decisions, you can earn an appreciable amount of money.

The experiment will proceed in three parts. Each part contains decision problems that require you to make a series of economic choices which determine your total earnings. The currency used in Part 1 of the experiment is U.S. Dollars. The currency used in Part 2 and 3 of the experiment is francs. Francs will be converted to U.S. Dollars at a rate of _50_ francs to _1_ dollar. At the end of today‟s experiment, you will be paid in private and in cash. 12 participants are in today‟s experiment.

It is very important that you remain silent and do not look at other people‟s work.

If you have any questions, or need assistance of any kind, please raise your hand and an experimenter will come to you. If you talk, laugh, exclaim out loud, etc., you will be asked to leave and you will not be paid. We expect and appreciate your cooperation.

At this time we proceed to Part 1 of the experiment.

INSTRUCTIONS FOR PART 1 YOUR DECISION

In this part of the experiment you will be asked to make a series of choices in decision problems. How much you receive will depend partly on chance and partly on the choices you make. The decision problems are not designed to test you. What we want to

know is what choices you would make in them. The only right answer is what you really would choose.

For each line in the table in the next page, please state whether you prefer option A or option B. Notice that there are a total of 15 lines in the table but just one line will be randomly selected for payment. You ignore which line will be paid when you make your choices. Hence you should pay attention to the choice you make in every line. After you have completed all your choices a token will be randomly drawn out of a bingo cage containing tokens numbered from 1 to 15. The token number determines which line is going to be paid.

Your earnings for the selected line depend on which option you chose: If you chose option A in that line, you will receive $1. If you chose option B in that line, you will receive either $3 or $0. To determine your earnings in the case you chose option B there will be second random draw. A token will be randomly drawn out of the bingo cage now containing twenty tokens numbered from 1 to 20. The token number is then compared with the numbers in the line selected (see the table). If the token number shows up in the left column you earn $3. If the token number shows up in the right column you earn $0.

Are there any questions?

Participant ID _________

INSTRUCTIONS FOR PART 2 YOUR DECISION

The second part of the experiment consists of 30 decision-making periods. At the beginning of each period, you will be randomly and anonymously placed into a group of 4 participants. The composition of your group will be changed randomly every period.

Each period, you and all other participants will be given an initial endowment of 60 francs. You will use this endowment to bid for a reward. The reward is worth 120 francs to you and the other three participants in your group. You may bid any integer number of francs between 0 and 60. An example of your decision screen is shown below.

Decision Screen

YOUR EARNINGS

After all participants have made their decisions, your earnings for the period are calculated. These earnings will be converted to cash and paid at the end of the experiment if the current period is one of the five periods that is randomly chosen for payment. If you receive the reward your period earnings are equal to your endowment plus the reward minus your bid. If you do not receive the reward your period earnings are equal to your endowment minus your bid.

If you receive the reward:

Earnings = Endowment + Reward – Your Bid = 60 + 120 – Your Bid If you do not receive the reward:

Earnings = Endowment – Your Bid = 60 – Your Bid

The more you bid, the more likely you are to receive the reward. The more the other participants in your group bid, the less likely you are to receive the reward.

Specifically, for each franc you bid you will receive one lottery ticket. At the end of each period the computer draws randomly one ticket among all the tickets purchased by 4 participants in the group, including you. The owner of the drawn ticket receives the reward of 120 francs. Thus, your chance of receiving the reward is given by the number of francs you bid divided by the total number of francs all 4 participants in your group bid.

Chance of receiving

the reward = Your Bid

Sum of all 4 Bids in your group

In case all participants bid zero, the reward is randomly assigned to one of the four participants in the group.

Example of the Random Draw

This is a hypothetical example used to illustrate how the computer is making a random draw. Let‟s say participant 1 bids 10 francs, participant 2 bids 15 francs, participant 3 bids 0 francs, and participant 4 bids 40 francs. Therefore, the computer assigns 10 lottery tickets to participant 1, 15 lottery tickets to participant 2, 0 lottery tickets to participant 3, and 40 lottery tickets for participant 4. Then the computer randomly draws one lottery ticket out of 65 (10 + 15 + 0 + 40). As you can see, participant 4 has the highest chance of receiving the reward: 0.62 = 40/65. Participant 2 has 0.23 = 15/65 chance, participant 1 has 0.15 = 10/65 chance, and participant 3 has 0 = 0/65 chance of receiving the reward.

After all participants make their bids, the computer will make a random draw which will decide who receives the reward. Then the computer will calculate your period earnings based on your bid and whether you received the reward or not.

At the end of each period, your bid, the sum of all bids in your group, whether you received the reward or not, and the earnings for the period are reported on the outcome screen as shown below. Once the outcome screen is displayed you should record your results for the period on your Personal Record Sheet under the appropriate heading.

Outcome Screen

IMPORTANT NOTES

You will not be told which of the participants in this room are assigned to which group. At the beginning of each period you will be randomly re-grouped with three other participants to form a four person group. You can never guarantee yourself the reward.

However, by increasing your contribution, you can increase your chance of receiving the reward. Regardless of who receives the reward, all participants will have to pay their bids.

At the end of the experiment we will randomly choose 5 of the 30 periods for actual payment in Part 2 using a bingo cage. You will sum the total earnings for these 5 periods and convert them to a U.S. dollar payment, as shown on the last page of your record sheet.

Are there any questions?

INSTRUCTIONS FOR PART 3

The third part of the experiment consists of 30 decision-making periods. The rules for part 3 are almost the same as the rules for part 2. At the beginning of each period, you will be randomly and anonymously placed into a group of 4 participants. The composition of your group will be changed randomly every period. Each period you will be given an initial endowment of 60 francs. The only difference is that in part 3, you will use this endowment to bid for two rewards (instead of one reward). The first reward is worth 90 francs and the second reward is worth 30 francs to you and the other three participants in your group. You may bid any integer number of francs between 0 and 60.

After all participants have made their decisions, your earnings for the period are calculated in the similar way as in part 2.

If you receive the first reward:

Earnings = Endowment + First Reward – Your Bid = 60+90–Your Bid If you receive the second reward:

Earnings = Endowment + Second Reward – Your Bid = 60+30–Your Bid If you do not receive either reward:

Earnings = Endowment – Your Bid = 60–Your Bid

The more you bid, the more likely you are to receive either first or second reward.

The more the other participants in your group bid, the less likely you are to receive any reward. Specifically, for each franc you bid you will receive one lottery ticket. At the end of each period the computer draws randomly one ticket among all the tickets purchased by 4 participants in the group, including you. The owner of the drawn ticket receives the first reward of 90 francs. Thus, your chance of receiving the first reward is given by the number of francs you bid divided by the total number of francs all 4 participants in your group bid.

Chance of receiving

the reward = Your Bid

Sum of all 4 Bids in your group

In case you do not receive the first reward there is a second draw for the second reward. For the second draw computer draws randomly one ticket among all the tickets purchased by 3 participants in the group who did not receive the first reward (the participant who received the first reward is excluded from the second draw). The owner of the drawn ticket receives the second reward of 30 francs. Your chance of receiving the second reward is given by the number of francs you bid divided by sum of 3 bids made by the participants who did not receive the first reward.

Chance of receiving the second reward =

Your Bid

Sum of all 3 Bids made by participants who did not receive the first reward

Each participant can win at most one reward. In case all participants bid zero, the first and the second reward is randomly assigned to two of the four participants in the group.

Example of the Random Draw

This is a hypothetical example used to illustrate how the computer is making a random draw. Let‟s say participant 1 bids 10 francs, participant 2 bids 15 francs, participant 3 bids 0 francs, and participant 4 bids 40 francs. Therefore, the computer assigns 10 lottery tickets to participant 1, 15 lottery tickets to participant 2, 0 lottery tickets to participant 3, and 40 lottery tickets for participant 4. Then, for the first random draw, the computer randomly draws one lottery ticket out of 65 (10 + 15 + 0 + 40). As you can see, participant 4 has the highest chance of receiving the first reward: 0.62 = 40/65. Participant 2 has 0.23 = 15/65 chance, participant 1 has 0.15 = 10/65 chance, and participant 3 has 0 = 0/65 chance of receiving the first reward.

After all participants make their bids, the computer makes a first random draw which decides who receives the first reward. Let‟s say that participant 4 has received the first reward. Then, for the second random draw, the computer randomly draws one lottery ticket out of 25 (10 + 15 + 0). Since participant 4 has already received first reward he is excluded from the second draw. Now, as you can see, participant 2 has the highest chance of receiving the second reward: 0.6 = 15/25. Participant 1 has 0.4 = 15/25 chance and participant 3 has 0 = 0/25 chance of receiving the second reward.

To summarize, all participants will make only one bid. After all participants have made their decisions, the computer will make two consecutive draws which will decide who receives the first and the second reward. Regardless of who receives the first and the second reward, all participants will have to pay their bids. Then the computer will calculate your period earnings based on your bid and whether you received either reward.

At the end of each period, your bid, the sum of all bids in your group, whether you received the first reward or not, whether you received the second reward or not, and the earnings for the period are reported on the outcome screen. Once the outcome screen is displayed you should record your results for the period on your Personal Record Sheet under the appropriate heading.

At the end of the experiment we will randomly choose 5 of the 30 periods for actual payment in Part 3 using a bingo cage. You will sum the total earnings for these 5 periods and convert them to a U.S. dollar payment, as shown on the last page of your record sheet.

Are there any questions?

ESSAY 2

EXPERIMENTAL COMPARISON OF MULTI-STAGE AND ONE-STAGE CONTESTS 2.1 Introduction

Contests are economic, political, or social interactive situations in which agents expend resources to receive a certain prize. Examples include marketing and advertising by firms, patent races, and rent-seeking activities. All these contests differ from one another on multiple dimensions including group size, number of prizes, number of inter-related stages, and rules that regulate interactions. The most popular theories investigating different aspects of contests are based on the seminal model of rent-seeking introduced by Tullock (1980). The main focus of rent-seeking literature is the relationship between the extent of rent dissipation and underlying contest characteristics (Nitzan, 1994).

The majority of rent-seeking studies are based on the assumption that contests last for only one stage. Many contests in practice, however, last for multiple stages. In each stage contestants expend costly efforts in order to advance to the final stage and win the prize. Two major purposes of our study are to compare the performance of a one-stage contest versus a two-stage elimination contest and to examine whether over-dissipation is observed in both stages of the two-stage contest.

We find that, contrary to the theory, the two-stage contest generates higher revenue and higher dissipation rates than the equivalent one-stage contest. Over-dissipation is observed in both stages of the two-stage contest and experience diminishes over-dissipation in the first stage but not in the second stage. Our experiment also provides evidence that winning is a component in a subject‟s utility. A simple behavioral model that accounts for a non-monetary utility of winning can explain significant over-dissipation in both contests. It can also explain why the two-stage contest generates higher revenue than the equivalent one-stage contest.

Recent theoretical models of multi-stage elimination contests reveal interesting dynamic aspects. Gradstein and Konrad (1999) consider a multi-stage elimination contest in which a number of parallel contests take place at each stage and only winners are promoted to the next stage. The authors show that, depending on the contest success function, a multi-stage contest may induce higher effort by the participants than a one-stage contest. Under a lottery contest success function, however, the two structures are equivalent. In the same line of research, Baik and Lee (2000) study a two-stage elimination contest with effort carryovers. In this contest, players in two groups compete non-cooperatively to win a prize. In the first stage, each group selects a finalist who competes for the prize in the second stage. First-stage efforts are partially (or fully) carried over to the second stage. Baik and Lee (2000) demonstrate that, in the case of player-specific carryovers, the rent-dissipation rate (defined as the ratio of the expended total effort to the value of the prize) increases in the carryover rate and the rent is fully dissipated with full carryover. Other theoretical studies of multi-stage elimination contests have been conducted by Rosen (1986), Clark and Riis (1996), Gradstein (1998),

Amegashie (1999), Stein and Rapoport (2005), Fu and Lu (2009), and Groh et al.

(2009).¹⁸ All these studies investigate different aspects of multi-stage contests such as elimination procedures, interdependency between the stages, asymmetry between contestants, and resource constraints.

Since rent-seeking behavior in the field is difficult to measure, researchers have turned to experimental testing of the theory, with almost all studies focused on one-stage contests (Millner and Pratt, 1989, 1991; Shogren and Baik, 1991; Davis and Reilly, 1998;

Potters et al., 1998; Anderson and Stafford, 2003).¹⁹ Despite considerable differences in experimental design among these studies, most share the major finding that aggregate rent-seeking behavior exceeds the equilibrium predictions.²⁰ Several researchers have offered explanations for such behavior based on non-monetary utility of winning (Parco et al., 2005), misperception of probabilities (Baharad and Nitzan, 2008), quantal response equilibrium, and heterogeneous risk preferences (Goeree et al., 2002; Sheremeta, 2009).

There are currently only a few experimental studies that investigate the performance of multi-stage contests.²¹ Schmitt et al. (2004) develop and experimentally test a model in which rent-seeking expenditures in the current stage affect the probability of winning a contest in both current and future stages. Two other experimental studies are based on a two-stage rent-seeking model developed by Stein and Rapoport (2005). In this model all players have budget constraints. In the first stage, players compete within their

18 Another type of multi-stage contests is the multi-battle contests. In a multi-battle contest, players compete in a sequence of simultaneous move contests to win a prize and the player whose number of victories reaches some given minimum number wins the prize. Such contests have been studied by Harris and Vickers (1985, 1987), Klumpp and Polborn (2006), and Konrad and Kovenock (2009).

19 For empirical results on multi-stage elimination tournaments in sports see Ehrenberg and Bognanno (1990) and Bognanno (2001).

20 Shogren and Baik (1991) do not find excessive expenditure.

21 Exception is a study by Amegashie et al. (2007) on multi-stage all-pay auction.

own groups by expending efforts, and the winner of each group proceeds to the second stage. In the second stage, players compete with one another to win a prize by expending additional efforts subject to budget constraints. The experimental studies of Parco et al.

(2005) and Amaldoss and Rapoport (2009) reject the equilibrium model of Stein and Rapoport (2005) because of significant over-dissipation in the first stage. Both experimental studies conjecture that the non-monetary utility of winning plays a crucial role in explaining excessive over-dissipation in the first stage. Our experimental design is based on Gradstein‟s and Konrad‟s (1999) theoretical model, which compares the performance of a one-stage contest versus a multi-stage elimination contest.

2.2 Theoretical Model

In a simple one-stage contest identical players are competing for a prize of value . Each risk-neutral player chooses his effort level, , to win the prize. The probability that a contestant wins the prize is given by a lottery contest success function:

. (1)

The contestant‟s probability of winning increases monotonically in own effort and decreases in the opponents‟ efforts. The expected payoff for risk-neutral player is given by

. (2)

That is, the probability of winning the prize, , times the value of the prize, , minus the effort expended, . Differentiating (2) with respect to and

accounting for the symmetric Nash equilibrium leads to a classical solution (Tullock, 1980),

. (3)

The simple model considered above is the building block of the contest theory.

Gradstein and Konrad (1999) extended this model to study a multi-stage elimination contest. In their contest, players expend irreversible efforts in attempt to advance to the final stage. In the first stage, all players are divided into several groups. The winner of

Gradstein and Konrad (1999) extended this model to study a multi-stage elimination contest. In their contest, players expend irreversible efforts in attempt to advance to the final stage. In the first stage, all players are divided into several groups. The winner of

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